{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c67e7915",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import emcee\n",
    "import celerite\n",
    "\n",
    "from celerite import terms\n",
    "from scipy.optimize import minimize\n",
    "c2='#f15a22'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f89fb889",
   "metadata": {},
   "outputs": [],
   "source": [
    "def log_like(params,y,gp,method):\n",
    "    gp.set_parameter_vector(params)\n",
    "    if method=='MAP':\n",
    "        return -gp.log_likelihood(y)+0.5*params[0]-params[1]*0.5\n",
    "    else: return -gp.log_likelihood(y)\n",
    "\n",
    "def log_probability(params,y,gp):\n",
    "        gp.set_parameter_vector(params)\n",
    "        lp=gp.log_prior()\n",
    "        log_a=gp.get_parameter_dict().get('kernel:log_a')\n",
    "        log_c=gp.get_parameter_dict().get('kernel:log_c')\n",
    "        if not np.isfinite(lp):\n",
    "            return -np.inf\n",
    "        return gp.log_likelihood(y)+lp-0.5*log_a+log_c*0.5\n",
    "\n",
    "\n",
    "def DRW_fit(t,s,err,method='MAX',tl=[1,5000],sl=[0.02,0.7]):\n",
    "    # Set up the GP model\n",
    "    bounds=dict(log_a=(2*np.log(sl[0]),2*np.log(sl[1])),\n",
    "                log_c=(-np.log(tl[1]),-np.log(tl[0])))\n",
    "    kernel=terms.RealTerm(log_a=np.log(0.1414),log_c=-np.log(400),bounds=bounds)\n",
    "    gp=celerite.GP(kernel,mean=np.mean(s),fit_mean=True)\n",
    "    gp.compute(t,err)\n",
    "    # Fit for the maximum likelihood parameters\n",
    "    initial_params = gp.get_parameter_vector()\n",
    "    soln=minimize(log_like, initial_params,method=\"L-BFGS-B\",args=(s,gp,method))\n",
    "    \n",
    "    gp.set_parameter_vector(soln.x)\n",
    "    rt=np.exp(-gp.get_parameter_dict().get('kernel:log_c'))#MLE or MAP\n",
    "    rs=np.exp(gp.get_parameter_dict().get('kernel:log_a')/2)\n",
    "    if method=='MLE' or method=='MAP':\n",
    "        return np.array([rt,rs])   \n",
    "    #MCMC\n",
    "    initial=np.array(soln.x)\n",
    "    ndim, nwalkers=len(initial),16\n",
    "    sampler=emcee.EnsembleSampler(nwalkers,ndim,log_probability,args=(s,gp))\n",
    "    #Running burn-in\n",
    "    p0=initial+1e-4*np.random.randn(nwalkers,ndim)\n",
    "    p0,lp,_=sampler.run_mcmc(p0,125)    \n",
    "    #Running production\n",
    "    sampler.reset()\n",
    "    sampler.run_mcmc(p0,500)\n",
    "    #Markov chains\n",
    "    t_chain=np.exp(np.sort(-sampler.flatchain[:,1]))\n",
    "    s_chain=np.exp(np.sort(sampler.flatchain[:,0]/2))\n",
    "    return t_chain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f09c5edb",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1103.7\n",
      "5.266414788397772e+261\n"
     ]
    }
   ],
   "source": [
    "y=np.loadtxt('141.5',usecols=[3,4,5])\n",
    "n=int(np.sqrt(len(y)))\n",
    "print(max(y[:,-1]))\n",
    "y[:,0:2]=np.power(10,y[:,0:2])\n",
    "y[:,2]=y[:,2]-500\n",
    "y[:,2]=np.exp(y[:,2])\n",
    "\n",
    "tl=np.logspace(np.log10(0.03),np.log10(0.03)+6,n)\n",
    "sl=np.logspace(np.log10(0.01),np.log10(30),n)\n",
    "\n",
    "tau=np.array([])\n",
    "for i in range(n):\n",
    "    tau=np.append(tau,np.trapz(y[n*i:(i+1)*n,2]/y[n*i,0]/y[n*i:(i+1)*n,1],y[n*i:(i+1)*n,1]))\n",
    "    #tau=np.append(tau,np.trapz(y[n*i:(i+1)*n,2],y[n*i:(i+1)*n,1]))\n",
    "norm=np.trapz(tau,tl)\n",
    "tau=tau/norm\n",
    "np.savetxt('with_prior',tau)\n",
    "print(norm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "a47ce68a",
   "metadata": {},
   "outputs": [],
   "source": [
    "x=np.loadtxt('lc05')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "750b48cc",
   "metadata": {},
   "outputs": [],
   "source": [
    "chain=DRW_fit(x[:,0],x[:,1],x[:,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "d906b0f2",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "232.1064502043746"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(chain)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "3677b536",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0002334724092294594"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(tau)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "1b982f0e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "91"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argmax(tau)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "411c16ae",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_8810/3429953507.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
      "  ax.set_xticklabels(range(0,1200,200),fontsize=15)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1280x960 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(dpi=200)\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(tl,tau,color=c2)\n",
    "ax.set_xlim(0,1000)\n",
    "ax.set_ylim(0,2.5e-4)\n",
    "ax.set_xlabel(r\"$\\tau$ / d\",fontsize=15)\n",
    "ax.set_xticklabels(range(0,1200,200),fontsize=15)\n",
    "ax.set_ylabel(r\"Proability(PRH)\",fontsize=15)\n",
    "ax.set_yticks(np.linspace(0,2e-4,5),\n",
    "              ['0',r'$5\\times10^{-5}$',r'$1\\times10^{-4}$',r'$1.5\\times10^{-4}$',r'$2\\times10^{-4}$'],\n",
    "              fontsize=15)\n",
    "\n",
    "ax2 = ax.twinx()\n",
    "ax2.hist(chain,density=True,bins=1410,range=(0.03,30000),alpha=0.5)\n",
    "ax2.plot(np.full(10,292),np.linspace(0,5e-3,10),'k--',lw=5,alpha=0.3)\n",
    "ax2.set_ylabel(r\"Proability(celerite)\",fontsize=15)\n",
    "ax2.set_xlim(0,1000)\n",
    "ax2.set_yticks(np.linspace(0,4e-3,3),\n",
    "               ['0',r'$2\\times10^{-3}$',r'$4\\times10^{-3}$'],fontsize=15)\n",
    "#ax2.set_xticks(range(0,1200,200),fontsize=15)\n",
    "\n",
    "fig.legend(['PRH',r'$\\tau_{\\rm in}$ = 292 d','celerite'],loc=2,bbox_to_anchor=(0.62,0.32),fontsize=13)\n",
    "\n",
    "ax.set_title(r'Marginalized Posteriors of $\\tau$ of PRH and celerite (N = 445, $\\sigma_e=\\sigma_{OGLE}$)',\n",
    "             fontsize=15)\n",
    "#ax2.set_xticks(range(0,1200,200),fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe2bdf67",
   "metadata": {},
   "source": [
    "另一种积分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "a5bfa1da",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.564552977660433e+263\n"
     ]
    }
   ],
   "source": [
    "y=np.loadtxt('141.5',usecols=[3,4,5])\n",
    "n=int(np.sqrt(len(y)))\n",
    "#y[:,0:2]=np.power(10,y[:,0:2])\n",
    "y[:,2]=y[:,2]-500\n",
    "y[:,2]=np.exp(y[:,2])\n",
    "\n",
    "tl=np.logspace(np.log10(0.03),np.log10(0.03)+6,n)\n",
    "sl=np.logspace(np.log10(0.01),np.log10(30),n)\n",
    "\n",
    "tau2=np.array([])\n",
    "for i in range(n):\n",
    "    #tau=np.append(tau,np.trapz(y[n*i:(i+1)*n,2]/y[n*i,0]/y[n*i:(i+1)*n,1],y[n*i:(i+1)*n,1]))\n",
    "    tau2=np.append(tau2,np.trapz(y[n*i:(i+1)*n,2]*np.power(10,y[n*i:(i+1)*n,1]),y[n*i:(i+1)*n,1]))\n",
    "    #print(np.trapz(y[n*i:(i+1)*n,2]*np.power(10,y[n*i:(i+1)*n,1]),y[n*i:(i+1)*n,1]))\n",
    "#print(tau2)\n",
    "norm2=np.trapz(tau2*tl,np.log10(tl))\n",
    "print(norm2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "f025c137",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "tau2=tau2/norm2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "6e448961",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.28868673e-162, 3.13154759e-162, 2.98356656e-162, 2.85002225e-162,\n",
       "       2.72673771e-162, 2.61835524e-162, 2.52698076e-162, 2.45893159e-162,\n",
       "       2.42056600e-162, 2.42090656e-162, 2.47143413e-162, 2.59321623e-162,\n",
       "       2.80748418e-162, 3.16151870e-162, 3.72660518e-162, 4.63055233e-162,\n",
       "       6.11319277e-162, 8.64255758e-162, 1.31938283e-161, 2.19274299e-161,\n",
       "       4.00375286e-161, 8.11528198e-161, 1.84593437e-160, 4.77368539e-160,\n",
       "       1.42310738e-159, 4.95733712e-159, 2.04874353e-158, 1.01844098e-157,\n",
       "       6.18484231e-157, 4.65901111e-156, 4.42103554e-155, 5.37172020e-154,\n",
       "       8.51623793e-153, 1.79473652e-151, 5.12303494e-150, 2.02132892e-148,\n",
       "       1.12389516e-146, 8.97244048e-145, 1.04409995e-142, 1.79586235e-140,\n",
       "       4.62192205e-138, 1.79335061e-135, 1.05603464e-132, 9.48411880e-130,\n",
       "       1.30254297e-126, 2.74009632e-123, 8.82426765e-120, 4.33168957e-116,\n",
       "       3.21365368e-112, 3.55487423e-108, 5.73742223e-104, 1.31171834e-099,\n",
       "       4.09239871e-095, 1.66296533e-090, 8.34809754e-086, 4.87510157e-081,\n",
       "       3.10907517e-076, 2.02806245e-071, 1.26688968e-066, 7.09944920e-062,\n",
       "       3.35572624e-057, 1.26031640e-052, 3.56376626e-048, 7.21525084e-044,\n",
       "       1.00218842e-039, 9.17064186e-036, 5.32663501e-032, 1.91909592e-028,\n",
       "       4.16095512e-025, 5.40032482e-022, 4.12076352e-019, 1.84967209e-016,\n",
       "       4.87403206e-014, 7.60948493e-012, 7.14533979e-010, 4.09411642e-008,\n",
       "       1.46206087e-006, 3.33062133e-005, 4.99526654e-004, 5.07860304e-003,\n",
       "       3.62002313e-002, 1.86392231e-001, 7.17653770e-001, 2.14257231e+000,\n",
       "       5.11153966e+000, 1.00386963e+001, 1.66996202e+001, 2.43336994e+001,\n",
       "       3.15038793e+001, 3.71298194e+001, 4.08296866e+001, 4.20135687e+001,\n",
       "       4.14468195e+001, 3.96020605e+001, 3.66023179e+001, 3.33794829e+001,\n",
       "       3.00520327e+001, 2.69867455e+001, 2.41131417e+001, 2.15882747e+001,\n",
       "       1.92093638e+001, 1.72349307e+001, 1.56050566e+001, 1.41540927e+001,\n",
       "       1.29205371e+001, 1.18609239e+001, 1.09566206e+001, 1.01883143e+001,\n",
       "       9.51519645e+000, 8.95338417e+000, 8.46698428e+000, 8.05663681e+000,\n",
       "       7.67358630e+000, 7.36908968e+000, 7.09804931e+000, 6.85629010e+000,\n",
       "       6.63385936e+000, 6.45726753e+000, 6.30575372e+000, 6.16781625e+000,\n",
       "       6.04568530e+000, 5.92629090e+000, 5.82128340e+000, 5.75113565e+000,\n",
       "       5.65825439e+000, 5.59217587e+000, 5.52566411e+000, 5.47068284e+000,\n",
       "       5.42867766e+000, 5.41230423e+000, 5.36234816e+000, 5.31083629e+000,\n",
       "       5.30513343e+000, 5.25616801e+000, 5.25234647e+000, 5.20567468e+000,\n",
       "       5.20011025e+000, 5.17153340e+000, 5.15387736e+000, 5.15208868e+000,\n",
       "       5.14836712e+000])"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tau2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "816532b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(tl,tau,lw=5)\n",
    "plt.plot(tl,tau2,'r--',alpha=0.5)\n",
    "plt.xlim(0,1000)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "84d5ec49",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
